Question

Find $p,q,r$ and $s$ if $\left[\begin{array}{cc}p+4& 2q-7\\ s-3& r+2s\end{array}\right]=\left[\begin{array}{cc}6& -3\\ 2& 14\end{array}\right]$

Answer 1

Two matrices are equal, if the corresponding elements are equal, i.e.,

$p+4=6\Rightarrow p=6-4=2$

$2q-7=-3\Rightarrow 2q=-3+7=4\Rightarrow q=2$

$s-3=2\Rightarrow s=5$

$r+2s=14\Rightarrow r+10=14\Rightarrow r=-4$